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Andru [333]
3 years ago
11

The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 mi

nutes. What is the probability that a randomly selected exam will require more than 15 minutes to grade
Mathematics
1 answer:
dem82 [27]3 years ago
8 0

Answer:

62.17% probability that a randomly selected exam will require more than 15 minutes to grade

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 16.3, \sigma = 4.2

What is the probability that a randomly selected exam will require more than 15 minutes to grade

This is 1 subtracted by the pvalue of Z when X = 15. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{15 - 16.3}{4.2}

Z = -0.31

Z = -0.31 has a pvalue of 0.3783.

1 - 0.3783 = 0.6217

62.17% probability that a randomly selected exam will require more than 15 minutes to grade

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